5x-3y=8 and 10x-6y=19
Answers
Answer:
5x-3y=8
5(1)-3(-1)=8
5+3=8
Therefore, x=1 and y=-1
Step-by-step explanation:
In the given pair of linear equations,
For first Equation:
a₁ = 5
b₁ = -3
c₁ = 8
\begin{gathered}\\\end{gathered}
For the second Equation:
a₂ = 10
b₂ = -6
c₂ = 19
\begin{gathered}\\\end{gathered}
For finding whether the equations have unique solution, infinitely many solutions or no solution let's compare the ratios.
Here,
\begin{gathered} \tt{\dfrac{5}{10} = \dfrac{ - 3}{ - 6} \neq \dfrac{8}{19}} \\ \\ \end{gathered}
10
5
=
−6
−3
=
19
8
\begin{gathered} \implies \tt{ \dfrac{1}{2} = \dfrac{1}{2} \neq \dfrac{8}{19} } \\ \\ \end{gathered}
⟹
2
1
=
2
1
=
19
8
\begin{gathered} \tt{ \dfrac{a _{1} }{a _{2}} = \dfrac{b_{1} }{b _{2} } \neq \dfrac{c _{1} }{c _{2} }} \\ \\ \end{gathered}
a
2
a
1
=
b
2
b
1
=
c
2
c
1
So, the given pair of linear equations does not have any solution.
KNOW MORE:
If a1/a2 = b1/b2 = c1/c2, then the given pair of linear equations would have infinitely many solutions.
If a1/a2 ≠ b1/b2 ≠ c1/c2, then the given pair of linear equations would have unique solution.